Atomic-Level and Surface Structure of Calcium Silicate Hydrate Nanofoils

Deciphering the calcium silicate hydrate (C-S-H) surface is crucial for unraveling the mechanisms of cement hydration and property development. Experimental observations of C-S-H in cement systems suggest a surface termination which is fundamentally different from the silicate-terminated surface assumed in many atomistic level studies. Here, a new multiparameter approach to describing the (001) basal C-S-H surface is developed, which considers how the surface termination affects the overall properties (Ca/Si ratio, mean chain length, relative concentration of silanol and hydroxide groups). Contrary to current beliefs, it is concluded that the (001) C-S-H surface is dominantly calcium terminated. Finally, an adsorption mechanism for calcium and hydroxide ions is proposed, which is in agreement with the surface charge densities observed in previous studies.


Surface construction
The Ca-Si chains for the surface are composed of the same groups of atoms (figure S1) as the upper and lower Ca-Si chains of the main layer. 1 Some of the different combinations of atom groups that can be used to form a single surface block are shown in figure S1a.Surface blocks 1 to 4 give a silicon termination of the C-S-H surface, where 1 and 2 show a block with the missing Q 2b site, and 5 to 8 give calcium termination, where we have a calcium in the bridging site (5   and 6), or calcium in the bridging site with an additional calcium next to it (7 and 8).The surface charge arises from the pH-dependent protonation of surface oxygens and deprotonation of chemisorbed water molecules 2 , which can be accounted for in the model as seen in pairs 1-2, 3-4 and 5-6, leading to a net charge.Although not shown in figure S1a, partial protonation and deprotonation, or additional hydroxides in the case of calcium termination are possible.Since classical molecular dynamics does not account for bond breakage and creation, the degree of silanol deprotonation as well as hydroxide presence on the surface needs to be chosen beforehand.Figure S1b  As is the case for the C-S-H bulk structure, 1 there can be many possible local arrangements of different surface blocks to build a representative C-S-H surface.Local arrangements here refer to the length of individual silicate chains (dimer, pentamer, …), the protonation of silanol groups and location of calcium and hydroxide ions at the surface.It is crucial that the constructed C-S-H structure (bulk with surface) mimics the experimental results as accurately as possible. 3][5][6][7][8][9][10] In particular the water structure at the surface will be directly related to the surface termination, and this will determine the hydrodynamic properties of flows through cement porosity, 3,11 since it can be substantially different to bulk water. 12
The round colored markers show the data points which were used to construct the atomic-scale model of the C-S-H nanofoils.The exact values of the markers are given in table S1.Table S1.Values which were taken for the construction of the C-S-H nanofoils through the manuscript.The values were chosen from the collected data by Duque-Redondo et al. 13 and are highlighted in figure S2.
Ca/Si MCL Si-OH/Si Ca-OH/Ca

C-S-H nanofoil with Mixed-Surface
This section provides a detailed explanation on how to construct a C-S-H nanofoil model with the (001) Mixed-Surface termination for any given Ca/Si ratio.
First the size of the system model needs to be specified: •  = number of defective tobermorite 14Å unit cells in a-axis direction •  = number of defective tobermorite 14Å unit cells in b-axis direction •  = number of calcium-silicate sheets (layers) in z-axis direction ( = 3 for 3 layers, 2 interlayers C-S-H) The mean chain length (MCL) is defined 1,23 as where   denotes either the exact number of given Q species in the atomistic model, or the proportion of Q species as given by 29 Si NMR. 23 is either 2, 2 or 1.Each Q 2b is always accompanied by two Q 2p silicates, therefore the MCL can be also written as The maximum amount of Q species (  ) for a given model of the nanofoil equals to where   stands for all the bridging sites, which are missing a Q 2b silicate, and are presumably occupied with a calcium atom.Due to the structure of the silicate chains, one third of the Q MAX are linking the dimers.This gives the next relation: Combining equations (2), (3) and (4) gives the number of Q 2b silicates, which is needed for ensuring the right MCL of the computational model (equation 5).The number of Q 2b silicates should be equally distributed between the calciumsilicate chains of the nanofoil.
where Q MAX is calculated from the parameters which decide the size of the atomistic system: From the total amount of silicates (Si) in the system: the needed amount of calcium (Ca) for a targeted Ca/Si ratio can be calculated as Assuming there is no calcium missing from the main layer calcium-silicate sheets, one can calculate the amount of calcium atoms which is in the interlayers and on the surfaces, while excluding the amount of calcium in the bridging sites (CaB): where: As seen in the review paper of Duque-Redondo et al. 13 and figure S2 the Si-OH/Si ratio decreases linearly with the increase in Ca/Si ratio.The linear fit of the experimental results (see figure S2) yields: Assuming a deprotonation rate of surface silanol groups (Dsurf = 0.9 for 90% deprotonation), the number of silanol groups in the interlayers can be calculated as: Finally, the amount of calcium which is associated with the interlayer and surface (equation 9), needs to be divided between them.The packing of the interlayers with calcium will depend on the desired Ca/Si ratio of the bulk (Ca/Sibulk):

Summary on constructing a C-S-H nanofoil with the (001) surfaces and targeted Ca/Si ratio
The C-S-H nanofoil was constructed with the in-house brick model code from Kunhi Mohamed et al. 1 (the code can be requested by contacting the authors).The example of the code is shown below.
Step-by-step guide to construct the nanofoil.
1. Define the targeted Ca/Si ratio and the size of the bulk C-S-H (number of layers -L, number of bricks in x-axis and y-axis direction -A and B).Use the Ca/Si ratio to define the MCL (figure S2).The MCL can also be calculated from the proportion of Q species (equation 2).
3. If starting from a CIF file of tobermorite 14 Å: 1. Multiply the tobermorite unit cell in the x, y and z-axis direction to create a super cell of L+2 thickness, A number of unit cells in x-axis direction and B number of unit cells in y-axis direction.
2. Delete the calcium silicate chains and interlayer Ca 2+ and H2O placed at zmin and zmax.With this a tobermorite nanofoil was constructed which has L layers and is terminated by (001) surfaces.
3. On each side of each layer remove CaB/(2L) number of Q 2b silicates and replace them with Ca 2+ ions.
The Q 2b silicates are removed by removing the Si atom and two O atoms, which are not shared with the neighboring silicates.Remaining Q 2b silicates should be equally distributed on the individual layers.
4. On the surface deprotonate Dsurf silanol groups.Start by deprotonating the upper silanol groups, followed by the lower (closer to the calcium oxide sheet) silanol groups.Silanol groups should be equally distributed on the surface.
5. On each interlayer surface distribute NSiOH Int /(L-1/L) silanol groups.The silanol groups should be attached to the non-sharing oxygens of the Q 2b silicates.Silanol groups should be equally distributed throughout the interlayer, firstly placed on the silicate oxygens which are closer to the calcium oxide sheet.
6.The tobermorite interlayer holds one Ca 2+ per brick.Add or remove so many Ca 2+ in the interlayers that the total amount of Ca 2+ (excluding CaB in the bridging sites) equals the calculated CaInt.Make sure each interlayer holds the same amount of Ca 2+ and that they are equally distributed through it.
7. Calculate the charge of each interlayer.By removing one hydrogen from the water molecule, you create an OH -ion which lowers the charge in the interlayer by -1 e. Create so many OH -ions to achieve charge neutrality of the bulk.Distribute the OH -equally through the interlayers.
8. If needed add additional H2O molecules to the interlayers to raise the 2H/Si ratio.Make sure to equally distribute the H2O molecules.
9. Close to each surface equally distribute Casurf/2 number of Ca 2+ .Between the placed Ca 2+ add OH -ions.
For charge neutral surface Casurf number of OH -should be placed.If a positive surface is desired, place less OH -ions, so many to obtain the desired surface charge.
10. Place a water slab above each surface.
4. If using the in-house brick model code: 1. Follow the same steps (1 to 8) as in step 3 to generate a description of the C-S-H nanofoil according to the brick model nomenclature (example below).Use this code to generate the model structure.
2. The brick code generates structures in DL Poly format which can be converted to XYZ format.This can be done for example with the visualization program VESTA. 24. Packmol 25 (uses XYZ data format) can then be used to insert Casurf/2 number of Ca 2+ and the desired number of OH -ions in the proximity of each surface.Packmol can be also used to insert a water slab between the surfaces.
Example of the Brick Model 1 code of a C-S-H nanofoil measuring 3 layers, 2 interlayers in the c-axis direction, 5 bricks in the x-axis direction and 6 bricks in the y-axis direction, without CaSurf on the surface.For a detailed description of the brick model we refer the reader to the publication of Kunhi Mohamed et al.

Force Field
In the following the force field parameters are listed.The force field is an improved version of the previous full charge force field of Valavi et al. 26 and Kunhi Mohamed et al. 27,28 The TIP4P/2005 water model 29 is used in conjunction with the SHAKE algorithm.All simulations were carried out with LAMMPS. 30For the description of the used interatomic potentials we refer the reader to the LAMMPS documentation 30 or the SI section of Valavi et al. 26 The kspace solver used was the pppm/tip4p with an accuracy of 1e-4.

Simulation protocol
Since the brick model inserts atoms in a predetermined way, which can result in atoms being in close proximity to each other, therefore experiencing large initial forces, a suitable equilibration protocol was used.CS ensemble refers to the core-shell equilibration.For the details on the core-shell equilibration we refer the reader to the work of Valavi et al. 26 The used thermostat is the Nose-Hoover with Tdamp values 100 times the timestep, while Pdamp was 1000 times the timestep.

Run Timestep [ps]
Number In the first run only calcium and water are thermostated.This is done with a smaller timestep so that the calcium and water can move away from the hydroxides (the code packs them relatively close).A slow equilibration follows, where the entire system is heated to the desired temperature.Next ( 4) is the core-shell equilibration, where the core-shell movement is decoupled and rescaled, which is necessary to prevent the overheating of core-shell pairs and keeping the total energy of the system constant. 31From ( 5) to ( 7) a series of NPT runs is carried out in order to relax the simulation box in the z-direction (obtaining bulk water properties), and x-y-directions for C-S-H structure relaxation.
The entire NPT run is carried out as a series of shorter runs, since due to the shrinkage of the simulation box the kspace mesh needs to be recalculated between the runs.Next (8-10) is the heating cycle which is necessary to overcome possible energetical barriers and reach a lower energy minimum.The timestep was lowered, since at the default 0.00028 ps the Oh-H bonds of surface silanol groups were broken.The last (12) run is the production run in which the density number of atomic species in z-direction are recorded, as well as trajectories and the radial distribution function.For more information we refer the reader to the LAMMPS input file (in.ZigaFF2)

Surface charge density
The surface charge density of the proposed model, shown in figure 5 of the main text, is calculated as follows.From table S11 the ionization fraction (α) at a given pH and surface silanol density (SSD) is chosen.From this the number of deprotonated silanol groups per surface area (DSG) is calculated as: The assumption follows the adsorption of  •  2+ and 2( − 2) •  − per deprotonated silanol group.Therefore, the surface charge density, σ, equals to: To examine Ca 2+ adsorption at the Si-Surface 2, the tobermorite 14 Å structure with the (001) surface was investigated.
We remind the reader, the basal (001) surface of tobermorite (cut through the interlayer) is the Si-Surface 2 in the present paper.The tobermorite structure was 3 layers, 2 interlayers thick, and placed in contact with a calciumchloride solution (figure S4).The (001) surface was modeled with 90% deprotonation of silanol groups.The negative surface charge was compensated with Ca 2+ ions (45 ions).Additional Ca 2+ ions (8 in total) and Cl -ions (16 ions) were placed between the surfaces.The surfaces were separated by approximately 80Å.All ions and water molecules were randomly placed between the surfaces. 25e inspection of the system reveals that approximately 14% of Ca 2+ were inner sphere adsorbed.Inner sphere adsorption here is defined as silicate oxygen (protonated or deprotonated) entering the first coordination shell of Ca 2+ , which happens when the distance between the calcium and oxygen is less than 3.15 Å. 32 The preferential outer sphere adsorption is further confirmed with the radial distribution function for calcium-oxygen (figure S5), where the first peak at approximately 2.4 Å points to inner sphere adsorption, while the intensity of the second peak at 4.7 Å points to preferred outer sphere adsorption (62% of Ca 2+ ).This can also be seen from the number density distribution along the z-axis (figure S5).24% of Ca 2+ remain in solution.Closer inspection of the adsorption sites reveals two mechanisms for inner sphere adsorption (figure S6).First is the adsorption on top of the Q 2p -Q 2p dimer, where Ca 2+ inner sphere adsorbs to the sharing oxygens of the silicates and an additional deprotonated silanol group.The deprotonated silanol group can be the upper non-sharing oxygen of the next in-chain Q 2b (shown in figure S6b), or the lower non-sharing oxygen of the neighboring silicate chain Q 2b .This adsorption site was first reported by Kalinichev et al. 12 , where they studied calcium adsorption on the tobermorite 9 Å (001) surface.A similar site was also observed by Kunhi Mohamed 33 in the C-S-H interlayer, who carried out a density functional theory study of the favorable calcium sites and reported this site as the energetically most favorable.The second inner sphere adsorption site (figure S6c) is due to only one silicate oxygen entering the first coordination shell of Ca 2+ .The upper silanol group was identified as highly acidic (pKa = 6.15), 34 where the solvent contribution for deprotonation is high.Further, Androniuk and Kalinichev carried out a metadynamics adsorption study, 35 where they identified this second site as energetically preferential for Ca 2+ adsorption.
The typical environment for outer sphere adsorption is shown in figure S6 with a triangle.Due to the structural characteristics of the tobermorite structure each next silicate chain is shifted in the b-axis direction by one silicate.
Therefore, looking in the a-axis direction a Q 2p -Q 2p dimer is neighboring a Q 2b silicate.The upper deprotonated silanol groups of the Q 2b silicates (corners of the triangle in figure S6) seem to be equally attractive to the calcium ion, positioning it approximately in the geometrical center of them.There are two distinguished heights of adsorption, as seen in figure S7a and the number density along z-axis direction in figure S5.The lower height is approximately at the same height as the upper deprotonated silanol group.(below 53 Å in figure S5) the resulting surface charge of the surface equals -1.2 e/nm 2 .

Calcium-Hydroxide Surface Network
The calcium-hydroxide network of the C-S-H (001) surface was investigated for the Ca/Si = 1.7 system, as described in the main text.To exclude possible effects of the initial configuration, two separate simulations with different initial configurations were carried out.The difference was in the initial placement of Ca 2+ and OH -next to the surface (see figure S7).The first (1) initial configuration had the calcium placed according to the adsorption sites in the literature. 12,33,35As explained in the previous section, those sites are Ca 2+ on top of the Q 2p -Q 2p (Q 1 -Q 1 ) dimer and on top of the Q 2b silicate.The OH -were placed in the proximity of the Individual calcium ions.The second (2) configuration had the same Mixed-Surface with CaB and Q 2b termination, although the required Ca 2+ and OH -were randomly placed in the 30 Å slab next to the surface.The ions, as well as the water molecules were inserted using Packmol. 25 both cases a similar calcium-hydroxide networks formed on the surface (figure S9).Both networks started to form in a similar manner, therefore only the first (1) initial configuration will be examined in the following discussion.The final configuration data files for both simulations are provided as part of the SI.Excluding CaB (calcium in the bridging site) 30% of the Ca 2+ are inner sphere adsorbed.Again, here we refer to inner sphere adsorption if a Ca 2+ is less than 3.15 Å away from a silicate oxygen (first shell coordination).Including CaB roughly 60 % of calcium at the surface is inner sphere adsorbed.As can be seen in figures S10 and S11, the inner sphere adsorption is exclusively associated with the adsorption on top of the Q 1 -Q 1 (Q 2p -Q 2p ) dimer, which was previously observed by Kalinichev et al. 12 The adsorption at the dimer site is further favored when the neighboring silicate chain carries the Q 2b species.However, in 50 % of the inner sphere adsorptions (CaB excluded) a hydroxide (OH -) is acting additionally as a bridge between the adsorbed Ca 2+ and the main layer calcium (figure S11, black arrow).
Figure S1.a) Possible C-S-H surface blocks, with net charge and building block notation 1 for the upper surface (in c direction); b) Mixed Ca-Si surface chain constructed from different surface blocks, (for the upper surface).Color code: Turquoise -calcium, dark blue -silicon, red -oxygen, white -hydrogen.

Figure S2 .
Figure S2.Collected experimental data by Duque-Redondo et al. 13 Colors correspond to the values which were used through the manuscript to construct the atomic-scale models of C-S-H nanofoils at a given Ca/Si and thickness.

Figure S3 .
Figure S3.Correlation of the overall Ca/Si ratio on the Ca/Si of the bulk structure for the 4 layers, 3 interlayers and 2 layers, 1 interlayer C-S-H structures with given (001) surfaces terminations.

Figure
Figure S5.Left: radial distribution function for calcium-silicate oxygen.Right: Number density in z-axis for calcium and silicates.The first silicate peak belongs to Q 2p while the second belongs to Q 2b silicates.

Figure S6 .
Figure S6.Location of inner (star) and outer (triangle) sphere adsorbed Ca 2+ .Everything beside the silicates and surface calcium is hidden for clarity.First shell coordination is shown with a bond.Color code: Ca-cyan, Si-blue, Ored, H-white.Labbez et al.9 predicted a surface charge of 4.5 e/nm 2 , for this type of surface at 90% deprotonation (pH 13) in contact with 2mM CaX2 solution (X being any monovalent anion).Accounting for all inner and outer sphere adsorbed Ca 2+

Figure S7 .
Figure S7.Initial configuration of the C-S-H nanofoil: 1) Ca 2+ located at the dimer and Q 2b adsorption sites and 2) Ca 2+ located on top of the deprotonated silanol groups, the remaining Ca 2+ and OH -are randomly inserted next to the surface.Color code: Ca-cyan, Si-blue, O-red, H-white.

Figure S8 .
Figure S8.Comparison of Ca-O and Ca-Ca radial distribution functions for the Si-Surface2 with Ca 2+ adsorption (orange) and the Mixed-Surface with Ca 2+ and OH -adsorption (blue).

Figure S9 .
Figure S9.Final configuration of the C-S-H nanofoil shown in figure S6.Color code: Ca-cyan, Si-blue, O-red, H-white.

Figure S10 .
Figure S10.Formation of the calcium-hydroxide network.CaB corresponds to the calcium in the bridging site.The star marks the inner sphere adsorbed calcium.Gray lines show the direction of the silicate chains (b-axis).Color code: Ca-cyan, Si-blue, O-red, H-white.

Figure S11 .
Figure S11.Typical inner sphere adsorption of calcium ions and the start of the calcium-hydroxide network.The star marks the inner sphere adsorbed calcium, CaB is calcium in the bridging site (linking dimers), and the arrow points to the hydroxide on the main layer calcium chains, which acts as a bridge for calcium adsorption.Gray lines show the direction of the silicate chains (b-axis).Color code: Ca-cyan, Si-blue, O-red, H-white.

3 Comparison of different thicknesses
surface 1.

Table S2
. Mean chain Length (MCL) and Ca/Si of investigated C-S-H nanofoils with overall Ca/Si = 1.7 and different surface terminations.

Table S11 .
9onization fraction (α) for different surface silanol densities (4.8, 2.8 and 0.8 OH/nm 2 ) and pHs as predicted by Grand Canonical Monte Carlo simulations for surfaces in contact with 2 mM CaX2 solutions9.X stands for any monovalent ion.
since the surface charge density without adsorbed calcium at the deprotonated silanols equals −  [e/nm 2 ], and after adsorption to +  [e/nm 2 ].